Mumax3 Script for Micromagnetic Simulation of Hybrid Py Nanodot and CoPd Matrix Structure with Variable Vertical Positioning

Abstract This repository contains a Mumax³ simulation script designed to model the magnetic behavior of a hybrid nanostructured system consisting of a Permalloy (Py) nanodot embedded into a circular anti-dot vacancy within a Cobalt-Palladium (CoPd) matrix. The script systematically investigates the ground-state magnetization profiles and relaxation processes of the Py nanodot as a function of its vertical displacement ($Z$-shift) relative to the CoPd layer under a varying out-of-plane external magnetic field. Technical Details & System Geometry Software Framework: Mumax³ (Micro-magnetic simulation software). Simulation Grid: 160 x 160 x 31 cells with a cell size of 2.5 x 2.5 x 1.0 nm. Boundary Conditions: Periodic Boundary Conditions (PBC) applied in the X and Y directions (SetPBC(2, 2, 0)). Materials Modeled: Region 1 (Py Nanodot): Diameter 50 nm, thickness 3 nm. Soft magnetic material parameters: M_s = 810 kA/m, A_ex = 10.5 pJ/m, alpha = 0.1. Region 2 (CoPd Matrix with Anti-dot): Matrix thickness 31 nm containing a circular anti-dot defect of diameter 60 nm where the Py dot is positioned. Hard magnetic material with Perpendicular Magnetic Anisotropy (PMA): M_s = 1 MA/m, A_ex = 20 pJ/m, K_u1 = 700 kJ/m³ along the Z-axis, alpha = 0.2. Simulation Protocol Geometry and Material Initialization: Defines the complementary geometry of the CoPd matrix layer and the shifting Py nanodot. Parametric Sweep over Vertical Shift ($Z$-Shift): The script executes a loop iterating the vertical alignment step-by-step to study how the physical overlap or depth of the Py dot inside the matrix affects its magnetic configuration. Demagnetization/Relaxation Sequence: * An external perpendicular magnetic field (B_ext) is applied along the Z-axis, decreasing cubically from 1.2 T down to 0T to guide the system towards equilibrium (minimize()). The state is recorded, followed by a sequence of small in-plane field pulses (B_x = 2 mT -> 5 mT ->2 mT -> 0 T) to overcome local energy barriers and resolve the true magnetic ground state of Region 1 (Py dot). Data Output: Saves magnetization configurations for Region 1 (m.Region(1)) under temporary names (Z_Shift[i]) and the finalized state (ground[i]) alongside standard tabulated data output (TableSave()).